1. Field of the Invention
The present invention relates to a method and a circuit for detecting displacements using micro-electromechanical sensors with compensation of parasitic capacitances and spurious displacements.
2. Description of the Related Art
As is known, the use of micro-electric-mechanical sensors, or MEMS sensors, with differential capacitive unbalance has been proposed for forming, for example, linear or rotational accelerometers and pressure sensors.
In particular, MEMS sensors of the indicated type comprise a fixed body (stator) and a moving mass, generally of suitably doped semiconductor material, connected to each other through elastic elements (springs) and restrained so that, with respect to the stator, the moving mass has predetermined translational and rotational degrees of freedom. Moreover, the stator and the moving mass have a plurality of fixed and, respectively, moving arms, interleaved to each other. In practice, each fixed arm is arranged between a pair of moving arms, so as to form a pair of capacitors having a common terminal and a capacitance which is a function of the relative position of the arms, that is of the relative position of the moving mass with respect to the stator. When the sensor is stressed, the moving mass moves and the capacitance of the capacitors is unbalanced.
Depending on the type of structure and relative movement allowed between the moving mass and the stator, it is possible to manufacture MEMS sensors of a linear or rotational type, with variable interspace (distance between each moving arm and the respective fixed arms) and/or with variable facing area (variation of the reciprocal facing area between the moving arms and the respective fixed arms).
In all mentioned cases, reading by the sensor (that is detection of an electric quantity representing the variation of the capacitance of the capacitors) leads to problems due to the presence of parasitic capacitors (pad and substrate capacitances). The reading precision is also limited by another drawback, which is caused by spurious displacements, i.e., displacements not according with the designed degrees of freedom and due to non-ideality of mechanical constraints.
For the sake of clarity, reference will be made to FIGS. 1 and 2, where a linear MEMS sensor 1 is shown; however, what will be explained hereinafter applies to MEMS sensors of any type.
In detail, the sensor 1 comprises a stator 2 and a moving mass 3, connected to each other by springs 4 so that the moving mass 3 can translate parallel to a first reference axis X, while it is substantially fixed with respect to a second and a third reference axes Y, Z. The sensor 1 is also symmetrical with respect to a longitudinal axis parallel to the first reference axis X.
The stator 2 and the moving mass 3 are provided with a plurality of first and second fixed arms 5xe2x80x2, 5xe2x80x3 and, respectively, with a plurality of moving arms 6, extending substantially parallel to the plane Y-Z.
As shown in detail in FIG. 2, each moving arm 6 is arranged between two respective fixed arms 5xe2x80x2, 5xe2x80x3, partially facing them. Consequently, the moving arm 6 forms, with the two fixed arms 5xe2x80x2, 5xe2x80x3, a first and, respectively, a second sensing capacitor 8, 9 with paraliel flat faces. In particular, the area of the plates of the sensing capacitors 8, 9 is equal to the facing area A of the moving arms 6 and of the fixed arms 5xe2x80x2, 5xe2x80x3. In particular, the facing area A is substantially a rectangle with sides Ly, Lz.
The first and the second sensing capacitor 8, 9 have a first and a second sensing capacitance Ca, Cb, respectively, given by the equations:                     Ca        =                  ϵ          ⁢                      A            X1                                              (        1        )                                Cb        =                  ϵ          ⁢                      A            X2                                              (        2        )            
where X1, X2 are the distances between the moving arm 6 and the first and, respectively, the second fixed arms 5xe2x80x2, 5xe2x80x3 of FIG. 2 and ∈ is the dielectric constant of the air.
In the sensor 1, all the sensing capacitances Ca formed between the moving arms 6 and the first fixed arms 5xe2x80x2 are parallel-connected; similarly all the sensing capacitances Cb formed between the moving arms 6 and the second fixed arms 5xe2x80x3 are parallel-connected. Consequently, altogether two capacitances are present between the stator 3 and the moving mass 4, equal to Cl=N*Ca and, respectively, to C2=N*Cb, with N number of moving arms 6 of the sensor 1. If we define as a common sensing capacitance Cs of the sensor 1 the value of the capacitances C1, C2 at rest, we have:
Cs=C1=C2xe2x80x83xe2x80x83(3)
After a movement of the moving arm 4 purely along the axis X, the sensing capacitances C1, C2 present variations with an opposite sign and with a same absolute value, and equal to a capacitive unbalance xcex94Cs.
In greater detail, supposing for simplicity""s sake that the distances X1, X2 are initially the same and equal to a rest distance X0, from equations (1)-(3) it results that the component xcex94Csx of the capacitive unbalance xcex94Cs according to the first reference axis X is given by the equation:                                           Δ            ⁢                          xe2x80x83                        ⁢            CSx                    =                                                    -                                                      ⅆ                    Cs                                                        ⅆ                    X                                                              ⁢              Δ              ⁢                              xe2x80x83                            ⁢              X                        =                                                                                ϵ                    ⁢                                          xe2x80x83                                        ⁢                    A                                                        X0                    2                                                  ⁢                Δ                ⁢                                  xe2x80x83                                ⁢                X                            =                                                Cs                  X0                                ⁢                Δ                ⁢                                  xe2x80x83                                ⁢                X                                                    ⁢                  
                ⁢                              Δ            ⁢                          xe2x80x83                        ⁢            CSx                    =                                                    -                                                      ⅆ                    Cs                                                        ⅆ                    X                                                              ⁢              Δ              ⁢                              xe2x80x83                            ⁢              X                        =                                                                                ϵ                    ⁢                                          xe2x80x83                                        ⁢                    A                                                        X0                    2                                                  ⁢                Δ                ⁢                                  xe2x80x83                                ⁢                X                            =                                                Cs                  X0                                ⁢                Δ                ⁢                                  xe2x80x83                                ⁢                X                                                                        (        4        )            
where xcex94X is the movement of the moving mass 4 long the first reference axis X.
In presence of a spurious movement xcex94Y parallel to the second reference axis Y, the capacitive unbalance xcex94Cs has a component xcex94Csy given by the equation:                               Δ          ⁢                      xe2x80x83                    ⁢          CSy                =                                            -                                                ⅆ                  Cs                                                  ⅆ                  Y                                                      ⁢            Δ            ⁢                          xe2x80x83                        ⁢            Y                    =                                                    -                                                      ϵ                    ⁢                                          xe2x80x83                                        ⁢                    Ly                                    X0                                            ⁢              Δ              ⁢                              xe2x80x83                            ⁢              Y                        =                                          -                                  CS                  Ly                                            ⁢              Δ              ⁢                              xe2x80x83                            ⁢              Y                                                          (        5        )            
Any spurious movements xcex94Z along the third reference axis Z are instead compensated by virtue of the axial symmetry of the sensor MEMS 1.
While the unbalance introduced by the movement xcex94X is of a differential type and is itself suitable to be detected by a fully differential sensing operational amplifier (see, for example, the article xe2x80x9cA Three-Axis Micromachined Accelerometer with a CMOS Position-Sense Interface and Digital Offset-Trim Electronicsxe2x80x9d by M. Lemkin, B. Boser, IEEE Journal of Solid-State Circuits, Vol. 34, N. 4, Pages 456-468), the movement xcex94Y introduces a notable common mode variation of the common sensing capacitance Cs, as it causes a variation of the facing area A (FIG. 2).
Since the sensing operational amplifier allows detection of a voltage that is directly proportional to the capacitive unbalance xcex94Cs, which in turn is directly proportional to the common sensing capacitance Cs, the common mode variation due to the movement xcex94Y introduces a significant sensing error.
An embodiment of the present invention overcomes the above-mentioned drawbacks.
According to an embodiment of the present invention, a method and a circuit are provided for detection of displacements through a micro-electromechanical sensor. The sensor includes a fixed body and a mobile mass, and forms a first sensing capacitor and a second sensing capacitor having a common capacitance at rest. The first and second sensing capacitors are connected to a first input terminal and, respectively, to a first output terminal and to a second output terminal of the sensing circuit.
According to an embodiment of the invention, the method includes the steps of closing a first negative-feedback loop, which is formed by the first and second sensing capacitors and by a differential amplifier, feeding an input of the differential amplifier with a staircase sensing voltage through driving capacitors so as to produce variations of an electrical driving quantity which are inversely proportional to the common sensing capacitance, and driving the sensor with the electrical driving quantity.
According to another embodiment of the invention, a circuit for detecting displacements in the sensor is provided, including a first negative-feedback loop, which can be closed selectively and which includes the first and second sensing capacitors and first amplifier means. The circuit also includes voltage-source means connected to the first amplifier means via capacitive driving means and supplying a staircase sensing voltage when the first negative-feedback loop is closed, so as to produce variations of an electrical driving quantity of the sensor, which are inversely proportional to the common sensing capacitance.